Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses just two extra qubits. Chamberland and Beverland (2018) provide a framework for flag error correction of arbitrary-distance codes. However, their construction requires conditions that only some code families are known to satisfy. We give a flag error-correction scheme that works for any stabilizer code, unconditionally. With fast qubit measurement and reset, it uses d+1 extra qubits for a distance-d code.
@article{arxiv.1912.09549,
title = {Flag fault-tolerant error correction for any stabilizer code},
author = {Rui Chao and Ben W. Reichardt},
journal= {arXiv preprint arXiv:1912.09549},
year = {2020}
}